1. Field of the Invention
This invention relates to the testing of underground formations or reservoirs. More particularly, this invention relates to a method for determining properties of the earth formation by interpreting fluid pressure and flow rate measurements.
2. Description of the Related Art
To obtain hydrocarbons such as oil and gas, boreholes are drilled by rotating a drill bit attached at a drill string end. A large proportion of the current drilling activity involves directional drilling, i.e., drilling deviated and horizontal boreholes to increase the hydrocarbon production and/or to withdraw additional hydrocarbons from the earth""s formations. Modern directional drilling systems generally employ a drill string having a bottomhole assembly (BHA) and a drill bit at an end thereof that is rotated by a drill motor (mud motor) and/or by rotating the drill string. A number of downhole devices placed in close proximity to the drill bit measure certain downhole operating parameters associated with the drill string. Such devices typically include sensors for measuring downhole temperature and pressure, azimuth and inclination measuring devices and a resistivity-measuring device to determine the presence of hydrocarbons and water. Additional down-hole instruments, known as logging-while-drilling (LWD) tools, are frequently attached to the drill string to determine the formation geology and formation fluid conditions during the drilling operations.
Drilling fluid (commonly known as the xe2x80x9cmudxe2x80x9d or xe2x80x9cdrilling mudxe2x80x9d) is pumped into the drill pipe to rotate the drill motor, provide lubrication to various members of the drill string including the drill bit and to remove cuttings produced by the drill bit. The drill pipe is rotated by a prime mover, such as a motor, to facilitate directional drilling and to drill vertical boreholes. The drill bit is typically coupled to a bearing assembly having a drive shaft, which in turn rotates the drill bit attached thereto. Radial and axial bearings in the bearing assembly provide support to the radial and axial forces of the drill bit.
Boreholes are usually drilled along predetermined paths and the drilling of a typical borehole proceeds through various formations. The drilling operator typically controls the surface-controlled drilling parameters, such as the weight on bit, drilling fluid flow through the drill pipe, the drill string rotational speed and the density and viscosity of the drilling fluid to optimize the drilling operations. The downhole operating conditions continually change and the operator must react to such changes and adjust the surface-controlled parameters to optimize the drilling operations. For drilling a borehole in a virgin region, the operator typically has seismic survey plots which provide a macro picture of the subsurface formations and a pre-planned borehole path. For drilling multiple boreholes in the same formation, the operator also has information about the previously drilled boreholes in the same formation.
Typically, the information provided to the operator during drilling includes borehole pressure and temperature and drilling parameters, such as Weight-On-Bit (WOB), rotational speed of the drill bit and/or the drill string, and the drilling fluid flow rate. In some cases, the drilling operator also is provided selected information about the bottom hole assembly condition (parameters), such as torque, mud motor differential pressure, torque, bit bounce and whirl etc.
Downhole sensor data are typically processed downhole to some extent and telemetered uphole by sending a signal through the drill string, or by mud-pulse telemetry which is transmitting pressure pulses through the circulating drilling fluid. Although mud-pulse telemetry is more commonly used, such a system is capable of transmitting only a few (1-4) bits of information per second. Due to such a low transmission rate, the trend in the industry has been to attempt to process greater amounts of data downhole and transmit selected computed results or xe2x80x9canswersxe2x80x9d uphole for use by the driller for controlling the drilling operations.
Commercial development of hydrocarbon fields requires significant amounts of capital. Before field development begins, operators desire to have as much data as possible in order to evaluate the reservoir for commercial viability. Despite the advances in data acquisition during drilling using the MWD systems, it is often necessary to conduct further testing of the hydrocarbon reservoirs in order to obtain additional data. Therefore, after the well has been drilled, the hydrocarbon zones are often tested with other test equipment.
One type of post-drilling test involves producing fluid from the reservoir, shutting-in he well, collecting samples with a probe or dual packers, reducing pressure in a test volume and allowing the pressure to build-up to a static level. This sequence may be repeated several times at several different depths or point within a single reservoir and/or at several different reservoirs within a given borehole. One of the important aspects of the data collected during such a test is the pressure build-up information gathered after drawing the pressure down. From these data, information can be derived as to permeability, and size of the reservoir. Further, actual samples of the reservoir fluid must be obtained, and these samples must be tested to gather Pressure-Volume-Temperature data and fluid properties such as density, viscosity and composition.
In order to perform these important tests, some systems require retrieval of the drill string from the borehole. Thereafter, a different tool, designed for the testing, is run into the borehole. A wireline is often used to lower the test tool into the borehole. The test tool sometimes utilizes packers for isolating the reservoir. Numerous communication devices have been designed which provide for manipulation of the test assembly, or alternatively, provide for data transmission from the test assembly. Some of those designs include mud-pulse telemetry to or from a downhole microprocessor located within, or associated with the test assembly. Alternatively, a wire line can be lowered from the surface, into a landing receptacle located within a test assembly, establishing electrical signal communication between the surface and the test assembly. Regardless of the type of test equipment currently used, and regardless of the type of communication system used, the amount of time and money required for retrieving the drill string and running a second test rig into the hole is significant. Further, if the hole is highly deviated, a wire line can not be used to perform the testing, because the test tool may not enter the hole deep enough to reach the desired formation.
A more recent system is disclosed in U.S. Pat. No. 5,803,186 to Berger et al. The ""186 patent provides a MWD system that includes use of pressure and resistivity sensors with the MWD system, to allow for real time data transmission of those measurements. The ""186 device allows obtaining static pressures, pressure build-ups, and pressure draw-downs with the work string, such as a drill string, in place. Also, computation of permeability and other reservoir parameters based on the pressure measurements can be accomplished without pulling the drill string.
The system described in the ""186 patent decreases the time required to take a test when compared to using a wireline. However, the ""186 patent does not provide an apparatus for improved efficiency when wireline applications are desirable. A pressure gradient test is one such test wherein multiple pressure tests are taken as a wireline conveys a test apparatus downward through a borehole. The purpose of the test is to determine fluid density in-situ and the interface or contact points between gas, oil and water when these fluids are present in a single reservoir.
Another apparatus and method for measuring formation pressure and permeability is described in U.S. Pat. No. 5,233,866 issued to Robert Desbrandes, hereinafter the ""866 patent. FIG. 1 is a reproduction of a figure from the ""866 patent that shows a drawdown test method for determining formation pressure and permeability.
Referring to FIG. 1, the method includes reducing pressure in a flow line that is in fluid communication with a borehole wall. In Step 2, a piston is used to increase the flow line volume thereby decreasing the flow line pressure. In other tools, such as that described by Michaels et al in U.S. Pat. No. 5,377,755, incorporated herein by reference, a pump is used to draw fluid from the formation. The rate of pressure decrease is such that formation fluid entering the flow line combines with fluid leaving the flow line to create a substantially linear pressure decrease. A xe2x80x9cbest straight line fitxe2x80x9d is used to define a straight-line reference for a predetermined acceptable deviation determination. The acceptable deviation shown is 2"sgr" from the straight line. Once the straight-line reference is determined, the volume increase is maintained at a steady rate. At a time t1, the pressure exceeds the 2"sgr" limit and it is assumed that the flow line pressure being below the formation pressure causes the deviation. At t1, the drawdown is discontinued and the pressure is allowed to stabilize in Step 3. At t2, another drawdown cycle is started which may include using a new straight-line reference. The drawdown cycle is repeated until the flow line stabilizes at a pressure twice. Step 5 starts at t4 and shows a final drawdown cycle for determining permeability of the formation. Step 5 ends at t5 when the flow line pressure builds up to the borehole pressure Pm. With the flow line pressure equalized to the borehole pressure, the chance of sticking the tool is reduced. The tool can then be moved to a new test location or removed from the borehole.
A drawback of the ""866 patent is that the time required for testing is too long due to stabilization time during the xe2x80x9cmini-buildup cycles.xe2x80x9d In the case of a low permeability formation, the stabilization may take from tens of minutes to even days before stabilization occurs. One or more cycles following the first cycle only compound the time problem.
Whether using wireline or MWD, the formation pressure and permeability measurement systems discussed above measure pressure by drawing down the pressure of a portion of the borehole to a point below the expected formation pressure in one step to a predetermined point well below the expected formation pressure or continuing the drawdown at an established rate until the formation fluid entering the tool stabilizes the tool pressure. Then the pressure is allowed to rise and stabilize by stopping the drawdown. The drawdown cycle may be repeated to ensure a valid formation pressure is being measured, and in some cases lost or corrupted data require retest. This is a time-consuming measurement process.
One method for measuring permeability and other parameters of a formation and fluid from such data is described in U.S. Pat. No. 5,708,204 issued to Ekrem Kasap, and assigned Western Atlas, hereinafter the ""204 patent and incorporated herein by reference. The ""204 patent describes a fluid flow rate analysis method for wireline formation testing tools, from which near-wellbore permeability, formation pressure (p*), and formation fluid compressibility are readily determined. When a formation rate analysis is performed using a piston to draw formation fluid, both pressure and piston displacement measurements as a function of time are analyzed using a multiple linear regression technique having the general form:
y=a0+a1xc2x7x1+a2xc2x7x2xe2x80x83xe2x80x83(1)
Commonly, the multiple linear regression is applied to the differential equation below in the following way:                                                         p              ⁢                              xe2x80x83                            ⁢                              (                t                )                                      ⏞                    y                =                                                            p                *                            ⏞                                      a              0                                ⁢                                                                                          -                                          η                                              k                        ⁢                                                  xe2x80x83                                                ⁢                                                  G                          0                                                ⁢                                                  xe2x80x83                                                ⁢                                                  r                          i                                                                                                      ⁢                                      xe2x80x83                                    ⁢                                      1                    C                                                  ⏞                                            a                1                                      ·                                                            V                  ·                                                            ⅆ                      p                                                              ⅆ                      t                                                                      ⏞                                            x                1                                              ⁢                                                                                          -                                          η                                              k                        ⁢                                                  xe2x80x83                                                ⁢                                                  G                          0                                                ⁢                                                  xe2x80x83                                                ⁢                                                  r                          i                                                                                                      ·                                      A                    piston                                                  ⏞                                            a                2                                      ·                                                                                ⅆ                    x                                                        ⅆ                    t                                                  ⏞                                            x                2                                                                        (        2        )            
(see Nomenclature section for symbol definitions)
The pressure p(t) in the draw down unit and the displacement x(t) of the draw down piston are available as a time series of measured data. From these data, the derivatives dp/dt and dx/dt are calculated for use in Eq. (2). Note that for systems using a pump to draw formation fluid, the term Apistonxc2x7dx/dt is replaced by q, the volumetric flow rate of the pump.
With common multiple linear regression techniques, the coefficients a0, a1 and a2 can be determined, which is the output of the formation rate analysis, as these coefficients contain all the desired information about the formation. The derivatives dp/dt and dx/dt are calculated numerically from the measured p(t) and x(t) data that is, in most cases, contaminated by noise. This noise represents a problem that deteriorates the result of the analysis substantially.
The methods of the present invention overcome the foregoing disadvantages of the prior art by providing a novel method for performing a multiple linear regression analysis of the measured data to provide a substantially more accurate correlation of the data.
The present invention contemplates a method for determining at least one parameter of interest of a formation surrounding a borehole. The method comprises conveying a tool into a borehole, where the borehole traverses a subterranean formation containing formation fluid under pressure. A probe is extended from the tool to the formation establishing hydraulic communication between the formation and a volume of a chamber in the tool. Fluid is withdrawn from the formation by increasing the volume of the chamber in the tool with a volume control device. Data sets are measured of a pressure of the fluid and the volume of the chamber as a function of time. Time derivatives are calculated of the measured pressure and the measured volume for each data set. A set of equations is generated comprising a multiple linear equation for each data set relating the measured pressure to a first term related to the time derivative of pressure and a second term related to the time derivative of volume. For each data set, the measured pressure comprises the corresponding measured pressure added to the sum of measured pressure of all preceding data sets; the first term comprises the corresponding time derivative of pressure added to the sum of time derivatives of pressure of all preceding data sets; and the second term comprises the corresponding time derivative of volume added to the sum of time derivatives of volume of all preceding data sets. A multiple linear regression is performed on the set of equations determining an intercept term, a first slope term associated with the first term, and a second slope term associated with the second term. Formation permeability, formation pressure, and fluid compressibility can be determined from the correlated data.
Examples of the more important features of the invention thus have been summarized rather broadly in order that the detailed description thereof that follows may be better understood, and in order that the contributions to the art may be appreciated. There are, of course, additional features of the invention that will be described hereinafter and which will form the subject of the claims appended hereto.